How to seperate Blenderkit Assets from Empty
Reasonably sure that Blenderkit uses instanced collections to instance its objects.  You should be able to use Make Instances Real to turn the instance into a real object.
That said, Blenderkit provides a specific way of doing what you want to do, and that's to go into the tool panel for it (N panel on the right, BlenderKit tab) and then in the Selected Model section press Bring to Scene.
Both seem to work although there is some difference in organisation - I believe the BlenderKit specific Bring to Scene recursively adds all of the model parts and materials, wheras Make Instances Real only seems to do one level, but I am not as certain on that.
Either way should hopefully be helpful to you.